But help me understand one thing - why does intensity factor do not taken into account when calculating how many calories been spent?

If we take two athletes one (A) have FTP 200 and another (B) FTP 250 and ask them to do same excersise, let's say 500 kJ/hour, obviously A will have higher TSS for that exercise and his average heartbeat will be higher.

Doesn't he supposed to use more calories that athlete B producing same 500 kJ/hour? If so for how much more? How to calculate that?

The answer is that there is no way to calculate it based on HR. The estimations that you can find will vary wildly, as each is based on a whole series of assumptions that are designed to give an average for the population - not useful at all for calculating what a particular person burns with any kind of precision or accuracy.

The only way to accurately assess calories is through the use of a power meter, as it objectively and precisely quantifies output (ie energy spent). Even then, however, there is a bit of a fudge factor, because even though 1 kJ is more or less equal to 1 kCal (or .9kCal), the precise efficiency at which a person converts calories into energy output varies. The range of variation across the population is reasonably small, and for an individual it can vary over the course of a season, so it is not that worth losing sleep over, but even in this case there is some loss of precision. Still, a power meter actually gives a meaningful quantification of calories burned, which HR cannot do.

The answer is that there is no way to calculate it based on HR. The estimations that you can find will vary wildly, as each is based on a whole series of assumptions that are designed to give an average for the population - not useful at all for calculating what a particular person burns with any kind of precision or accuracy.

This is generally true. Firstbeat, a Finnish company, claims to have developed an algorithm that is much more accurate than the traditional HRM equations and that adapts to an athlete's performance as measured by GPS devices. It works by measuring the intervals between individual heartbeats and analyzing changes in them. This white paper describes the technology (in general terms, since it's a trade secret). Firstbeat claims an error of 7-10% vs. direct calorimetry; for comparison, the indirect calorimetry done in many fitness testing labs has an error around 5% (according to the white paper).

I've noticed that my Garmin Edge 800 and Forerunner 620, which use Firstbeat's technology, produce calorie estimates that are much lower than other HRMs and that are comparable, for cycling, to estimates from stationary ergometers.

If we take two athletes one (A) have FTP 200 and another (B) FTP 250 and ask them to do same excersise, let's say 500 kJ/hour, obviously A will have higher TSS for that exercise and his average heartbeat will be higher.

Doesn't he supposed to use more calories that athlete B producing same 500 kJ/hour? If so for how much more? How to calculate that?

As mentioned above, the conversion factor from kJ/hour to calories varies from person to person, but it does not vary much (the variation is about 5-10%) and it does not correlate with FTP. (The biggest residual is actually cadence. All else equal, you burn about 60 more calories per hour pedaling at 100 rpm than when pedaling at 60 rpm.)

If you're looking at this from the weight loss point of view, if you shoot for a 1000 calorie/day deficit with 500 calories from exercise and 500 calories from diet, the uncertainty in power meter based deficit is about 50 calories - basically insignificant.

(This all applies to exercise below lactate threshold. Once you go above lactate threshold, things get more complicated.)

This is kind of interesting. My wife and I ride a tandem. Calculating power output by my times on my single and tandem up known long climbs last summer, I'm about twice as strong as my wife in watts output. For our tandem team, Strava gives an estimate of kJ and also shows a calculated burn. IIRC, the previous Strava version showed the calories calculated by the device, in my case a Garmin 800. This was the same calories displayed by TrainingPeaks. The new version of Strava now shows a burn that is 1.115 * calculated kJ, or it does for us. However, the Garmin device reads my HR, which shows a much smaller burn just for me, which makes sense. Our team burn as calculated by Strava runs ~45-50 calories/mile, while my personal burn calculated by my Garmin runs about 25-27 kCal/mile. These are all in hilly terrain. I think my personal burn should be quite a bit higher, closer to 40 kCal/mile or more, as I am much faster at the same HR on my single.

In any case, I don't pay too much attention to that. I just watch my scale.

As to the OP's question, no intensity factor doesn't matter. Assuming the two athletes weigh the same, they will burn the same if they ride at the same speed, even though one is having a lung up and the other cruising. Strava will show the same kJ for each. An assuming as noted above that they stay aerobic.

I borrowed and rode with a PM for a number of rides and compared calories burned based on joule output (using the accepted correction factors for physiological efficiency) to the HR formula in OP's method 1 and found I needed to multiply the HR formula result by 0.7 to get results close to the PM based calculations. With the 0.7 correction factor, the HR formula produced calorie consumption in reasonably close agreement with the PM results over a variety of rides including rides 25-100 miles in length, those with and without a lot of climbing, and fast pace and moderated pace rides.

This suggests to me that the HR formula can work well enough once calibrated to the individual.

I borrowed and rode with a PM for a number of rides and compared calories burned based on joule output (using the accepted correction factors for physiological efficiency) to the HR formula in OP's method 1 and found I needed to multiply the HR formula result by 0.7 to get results close to the PM based calculations. With the 0.7 correction factor, the HR formula produced calorie consumption in reasonably close agreement with the PM results over a variety of rides including rides 25-100 miles in length, those with and without a lot of climbing, and fast pace and moderated pace rides.

This suggests to me that the HR formula can work well enough once calibrated to the individual.

What did you plug into the formula for VO2max, W and A?

As quoted, the formula does not make a whole lot of sense to me. You should not be adding contributions of VO2max, heart rate and weight (assuming that W is weight), you should be multiplying them, like so:

Here you insert weight in kg, T in minutes, VO2max and VO2resting in ml/(kg*min). You can assume VO2resting ~ 3.5. (But, since you probably don't know your VO2max anyway, you might as well simply treat the whole VO2max-VO2resting term as an unknown, and tweak it to see what value gives you a good fit.) In my experiments, the fit is better if HRresting is not your "real" resting HR but the heart rate you see when you sit on the bike without moving (70-80 ish). If you fiddle with VO2max and HRresting, you can get a pretty good agreement with power meter data, within 10%.